Subgroups — C₃×#33073 #10651680

Order 768.

750 conjugacy classes of subgroups.

The subgroup lattice has 462 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#2859	C₂	1	1	yes	maximal, characteristic
2	C₃×C₄²×Q₈	C₂	1	1	yes	maximal, characteristic
3	C₃×#1948	C₂	1	1	yes	maximal, characteristic
4	C₃×#1947	C₂	1	1	yes	maximal, characteristic
5	C₃×#1920	C₂	1	2	yes	maximal
6	C₃×#1918	C₂	1	2	yes	maximal
7	C₃×#1865	C₂	1	2	yes	maximal
8	C₃×#1863	C₂	1	2	yes	maximal
9	C₃×#1831	C₂	1	1	yes	maximal, characteristic
10	C₃×#1803	C₂	1	1	yes	maximal, characteristic
11	C₃×#1803	C₂	1	1	yes	maximal, characteristic
12	#33073	C₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
13	C₂×C₃×#125	—	2	1	no	—
14	C₂×C₃×C₄×Q₈	C₂²	1	1	yes	characteristic
15	C₂×C₃×C₄×Q₈	C₂²	1	1	yes	characteristic
16	C₂×C₃×C₄×Q₈	C₂²	1	1	yes	characteristic
17	C₂×C₃×#107	C₂²	1	2	yes	—
18	C₂×C₃×#106	C₂²	1	2	yes	—
19	C₂×C₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
20	C₂×C₃×C₄⋊C₈	C₂²	1	1	yes	characteristic
21	C₂×C₃×#103	C₂²	1	2	yes	—
22	C₂×C₃×#103	C₂²	1	2	yes	—
23	C₃×#389	—	2	1	no	—
24	C₃×#389	—	2	1	no	—
25	C₃×#389	C₂²	1	2	yes	—
26	C₃×#389	C₂²	1	2	yes	—
27	C₃×#384	C₂²	1	1	yes	characteristic
28	C₃×#384	C₂²	1	1	yes	characteristic
29	C₃×#382	—	2	1	no	—
30	C₃×C₄×C₄⋊C₄	—	2	1	no	—
31	C₃×C₄×C₄⋊C₄	—	2	1	no	—
32	C₃×C₄×C₄⋊C₄	—	2	1	no	—
33	C₃×C₄×C₄⋊C₄	C₂²	1	1	yes	characteristic
34	C₃×C₄×C₄⋊C₄	C₂²	1	1	yes	characteristic
35	C₃×C₄×C₄⋊C₄	C₂²	1	1	yes	characteristic
36	C₃×C₄³	—	2	1	no	—
37	C₃×C₄³	C₂²	1	1	yes	characteristic
38	C₃×#340	C₂²	1	2	yes	—
39	C₃×#340	C₂²	1	2	yes	—
40	C₃×#340	C₂²	1	2	yes	—
41	C₃×#340	C₂²	1	2	yes	—
42	C₃×#336	C₂²	1	2	yes	—
43	C₃×#336	C₂²	1	2	yes	—
44	#2859	C₂×C₃	1	1	yes	characteristic
45	C₄²×Q₈	C₂×C₃	1	1	yes	characteristic
46	#1948	C₂×C₃	1	1	yes	characteristic
47	#1947	C₂×C₃	1	1	yes	characteristic
48	#1920	C₂×C₃	1	2	yes	—
49	#1918	C₂×C₃	1	2	yes	—
50	#1865	C₂×C₃	1	2	yes	—
51	#1863	C₂×C₃	1	2	yes	—
52	#1831	C₂×C₃	1	1	yes	characteristic
53	#1803	C₂×C₃	1	1	yes	characteristic
54	#1803	C₂×C₃	1	1	yes	characteristic
55	C₂²×C₃×Q₈	C₂³	1	1	yes	characteristic
56	C₂²×C₃×C₈	C₂³	1	2	yes	—
57	C₂²×C₃×C₈	C₂³	1	2	yes	—
58	C₃×#125	—	4	4	no	—
59	C₃×C₄×Q₈	—	2	2	no	—
60	C₃×C₄×Q₈	—	2	2	no	—
61	C₃×C₄×Q₈	—	2	2	no	—
62	C₃×C₄×Q₈	—	2	2	no	—
63	C₃×C₄×Q₈	—	2	2	no	—
64	C₃×C₄×Q₈	Q₈	1	4	yes	—
65	C₂×C₃×C₄⋊C₄	—	2	1	no	—
66	C₂×C₃×C₄⋊C₄	—	2	1	no	—
67	C₂×C₃×C₄⋊C₄	—	2	1	no	—
68	C₂×C₃×C₄⋊C₄	—	2	1	no	—
69	C₂×C₃×C₄⋊C₄	—	2	1	no	—
70	C₂×C₃×C₄⋊C₄	—	2	1	no	—
71	C₂×C₃×C₄⋊C₄	—	2	1	no	—
72	C₂×C₃×C₄⋊C₄	—	2	2	no	—
73	C₂×C₃×C₄⋊C₄	—	2	2	no	—
74	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
75	C₂×C₃×C₄⋊C₄	C₂³	1	2	yes	—
76	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
77	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
78	C₂×C₃×C₄⋊C₄	C₂³	1	1	yes	characteristic
79	C₂×C₃×C₄²	—	2	1	no	—
80	C₂×C₃×C₄²	—	2	1	no	—
81	C₂×C₃×C₄²	—	2	1	no	—
82	C₂×C₃×C₄²	—	2	1	no	—
83	C₂×C₃×C₄²	—	2	1	no	—
84	C₂×C₃×C₄²	—	2	1	no	—
85	C₂×C₃×C₄²	D₄	1	1	yes	characteristic
86	C₂×C₃×C₄²	D₄	1	1	yes	characteristic
87	C₂×C₃×C₄²	D₄	1	1	yes	characteristic
88	C₂×C₃×C₄²	D₄	1	1	yes	characteristic
89	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
90	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
91	C₂×C₃×C₄²	C₂³	1	1	yes	characteristic
92	C₃×#107	—	2	4	no	—
93	C₃×#106	—	2	4	no	—
94	C₃×C₄⋊C₈	—	2	2	no	—
95	C₃×C₄⋊C₈	—	2	2	no	—
96	C₃×#103	—	2	4	no	—
97	C₃×#103	—	2	4	no	—
98	C₃×#95	—	2	1	no	—
99	C₃×#95	—	2	1	no	—
100	C₃×#95	—	2	1	no	—
101	C₃×#95	—	2	2	no	—
102	C₃×#95	—	2	2	no	—
103	C₂×#125	—	2	1	no	—
104	C₂×C₄×Q₈	C₂²×C₃	1	1	yes	characteristic
105	C₂×C₄×Q₈	C₂²×C₃	1	1	yes	characteristic
106	C₂×C₄×Q₈	C₂²×C₃	1	1	yes	characteristic
107	C₂×#107	C₂²×C₃	1	2	yes	—
108	C₂×#106	C₂²×C₃	1	2	yes	—
109	C₂×C₄⋊C₈	C₂²×C₃	1	1	yes	characteristic
110	C₂×C₄⋊C₈	C₂²×C₃	1	1	yes	characteristic
111	C₂×#103	C₂²×C₃	1	2	yes	—
112	C₂×#103	C₂²×C₃	1	2	yes	—
113	#389	—	2	1	no	—
114	#389	—	2	1	no	—
115	#389	C₂²×C₃	1	2	yes	—
116	#389	C₂²×C₃	1	2	yes	—
117	#384	C₂²×C₃	1	1	yes	characteristic
118	#384	C₂²×C₃	1	1	yes	characteristic
119	#382	—	2	1	no	—
120	C₄×C₄⋊C₄	—	2	1	no	—
121	C₄×C₄⋊C₄	—	2	1	no	—
122	C₄×C₄⋊C₄	—	2	1	no	—
123	C₄×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
124	C₄×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
125	C₄×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
126	C₄³	—	2	1	no	—
127	C₄³	C₂²×C₃	1	1	yes	characteristic
128	#340	C₂²×C₃	1	2	yes	—
129	#340	C₂²×C₃	1	2	yes	—
130	#340	C₂²×C₃	1	2	yes	—
131	#340	C₂²×C₃	1	2	yes	—
132	#336	C₂²×C₃	1	2	yes	—
133	#336	C₂²×C₃	1	2	yes	—
134	C₂×C₃×Q₈	—	2	1	no	—
135	C₂×C₃×Q₈	—	2	1	no	—
136	C₂×C₃×Q₈	—	2	1	no	—
137	C₂×C₃×Q₈	C₂×Q₈	1	2	yes	—
138	C₂×C₃×Q₈	#41	1	2	yes	—
139	C₂×C₃×Q₈	#41	1	2	yes	—
140	C₂²×C₃×C₄	—	2	1	no	—
141	C₂²×C₃×C₄	—	2	1	no	—
142	C₂²×C₃×C₄	—	2	1	no	—
143	C₂²×C₃×C₄	—	2	1	no	—
144	C₂²×C₃×C₄	—	2	2	no	—
145	C₂²×C₃×C₄	—	2	2	no	—
146	C₂²×C₃×C₄	C₂×D₄	1	1	yes	characteristic
147	C₂²×C₃×C₄	C₂×D₄	1	1	yes	characteristic
148	C₂²×C₃×C₄	C₂×D₄	1	1	yes	characteristic
149	C₂²×C₃×C₄	C₂×D₄	1	1	yes	characteristic
150	C₂²×C₃×C₄	C₂×D₄	1	1	yes	characteristic
151	C₂²×C₃×C₄	C₂×D₄	1	1	yes	characteristic
152	C₂²×C₃×C₄	C₂⁴	1	1	yes	characteristic
153	C₂×C₃×C₈	—	2	2	no	—
154	C₂×C₃×C₈	—	2	2	no	—
155	C₂×C₃×C₈	—	2	2	no	—
156	C₂×C₃×C₈	—	2	2	no	—
157	C₂×C₃×C₈	—	2	2	no	—
158	C₂×C₃×C₈	—	2	2	no	—
159	C₃×C₄⋊C₄	—	2	4	no	—
160	C₃×C₄⋊C₄	—	2	4	no	—
161	C₃×C₄⋊C₄	—	2	4	no	—
162	C₃×C₄⋊C₄	—	2	1	no	—
163	C₃×C₄⋊C₄	—	2	1	no	—
164	C₃×C₄⋊C₄	—	2	1	no	—
165	C₃×C₄⋊C₄	—	2	2	no	—
166	C₃×C₄⋊C₄	—	2	2	no	—
167	C₃×C₄⋊C₄	—	2	2	no	—
168	C₃×C₄⋊C₄	—	2	2	no	—
169	C₃×C₄⋊C₄	—	4	2	no	—
170	C₃×C₄⋊C₄	—	4	2	no	—
171	C₃×C₄⋊C₄	—	4	4	no	—
172	C₃×C₄⋊C₄	—	4	2	no	—
173	C₃×C₄⋊C₄	—	4	4	no	—
174	C₃×C₄⋊C₄	—	4	2	no	—
175	C₃×C₄⋊C₄	C₂×Q₈	1	2	yes	—
176	C₃×C₄⋊C₄	#41	1	2	yes	—
177	C₃×C₄⋊C₄	#41	1	2	yes	—
178	C₃×C₄²	—	2	4	no	—
179	C₃×C₄²	—	2	4	no	—
180	C₃×C₄²	—	2	4	no	—
181	C₃×C₄²	—	2	2	no	—
182	C₃×C₄²	—	2	2	no	—
183	C₃×C₄²	—	2	2	no	—
184	C₃×C₄²	—	2	2	no	—
185	C₃×C₄²	—	2	1	no	—
186	C₃×C₄²	—	2	1	no	—
187	C₃×C₄²	—	2	1	no	—
188	C₃×C₄²	—	2	1	no	—
189	C₃×C₄²	—	4	2	no	—
190	C₃×C₄²	—	4	2	no	—
191	C₃×C₄²	—	4	2	no	—
192	C₃×C₄²	C₂×Q₈	1	2	yes	—
193	C₃×C₄²	#41	1	2	yes	—
194	C₂²×Q₈	C₂³×C₃	1	1	yes	characteristic
195	C₂²×C₈	C₂³×C₃	1	2	yes	—
196	C₂²×C₈	C₂³×C₃	1	2	yes	—
197	#125	—	4	4	no	—
198	C₄×Q₈	—	2	2	no	—
199	C₄×Q₈	—	2	2	no	—
200	C₄×Q₈	—	2	2	no	—
201	C₄×Q₈	—	2	2	no	—
202	C₄×Q₈	—	2	2	no	—
203	C₄×Q₈	C₃×Q₈	1	4	yes	—
204	C₂×C₄⋊C₄	—	2	1	no	—
205	C₂×C₄⋊C₄	—	2	1	no	—
206	C₂×C₄⋊C₄	—	2	1	no	—
207	C₂×C₄⋊C₄	—	2	1	no	—
208	C₂×C₄⋊C₄	—	2	1	no	—
209	C₂×C₄⋊C₄	—	2	2	no	—
210	C₂×C₄⋊C₄	—	2	2	no	—
211	C₂×C₄⋊C₄	—	2	1	no	—
212	C₂×C₄⋊C₄	—	2	1	no	—
213	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
214	C₂×C₄⋊C₄	C₂³×C₃	1	2	yes	—
215	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
216	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
217	C₂×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
218	C₂×C₄²	—	2	1	no	—
219	C₂×C₄²	—	2	1	no	—
220	C₂×C₄²	—	2	1	no	—
221	C₂×C₄²	—	2	1	no	—
222	C₂×C₄²	—	2	1	no	—
223	C₂×C₄²	—	2	1	no	—
224	C₂×C₄²	C₃×D₄	1	1	yes	characteristic
225	C₂×C₄²	C₃×D₄	1	1	yes	characteristic
226	C₂×C₄²	C₃×D₄	1	1	yes	characteristic
227	C₂×C₄²	C₃×D₄	1	1	yes	characteristic
228	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
229	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
230	C₂×C₄²	C₂³×C₃	1	1	yes	characteristic
231	#107	—	2	4	no	—
232	#106	—	2	4	no	—
233	C₄⋊C₈	—	2	2	no	—
234	C₄⋊C₈	—	2	2	no	—
235	#103	—	2	4	no	—
236	#103	—	2	4	no	—
237	#95	—	2	1	no	—
238	#95	—	2	1	no	—
239	#95	—	2	1	no	—
240	#95	—	2	2	no	—
241	#95	—	2	2	no	—
242	C₂³×C₃	C₂²×D₄	1	1	yes	characteristic
243	C₃×Q₈	—	2	2	no	—
244	C₃×Q₈	—	2	2	no	—
245	C₃×Q₈	—	2	2	no	—
246	C₃×Q₈	#125	1	4	yes	complemented
247	C₂×C₃×C₄	—	2	2	no	—
248	C₂×C₃×C₄	—	2	1	no	—
249	C₂×C₃×C₄	—	2	1	no	—
250	C₂×C₃×C₄	—	2	2	no	—
251	C₂×C₃×C₄	—	2	2	no	—
252	C₂×C₃×C₄	—	2	1	no	—
253	C₂×C₃×C₄	—	2	1	no	—
254	C₂×C₃×C₄	—	2	1	no	—
255	C₂×C₃×C₄	—	2	1	no	—
256	C₂×C₃×C₄	—	2	2	no	—
257	C₂×C₃×C₄	—	2	1	no	—
258	C₂×C₃×C₄	—	2	1	no	—
259	C₂×C₃×C₄	—	2	2	no	—
260	C₂×C₃×C₄	—	2	2	no	—
261	C₂×C₃×C₄	—	2	1	no	—
262	C₂×C₃×C₄	—	2	1	no	—
263	C₂×C₃×C₄	—	2	1	no	—
264	C₂×C₃×C₄	—	2	1	no	—
265	C₂×C₃×C₄	—	4	1	no	—
266	C₂×C₃×C₄	—	4	1	no	—
267	C₂×C₃×C₄	—	4	1	no	—
268	C₂×C₃×C₄	—	4	1	no	—
269	C₂×C₃×C₄	—	4	1	no	—
270	C₂×C₃×C₄	—	4	1	no	—
271	C₂×C₃×C₄	—	4	2	no	—
272	C₂×C₃×C₄	—	4	2	no	—
273	C₂×C₃×C₄	—	4	2	no	—
274	C₂×C₃×C₄	—	4	2	no	—
275	C₂×C₃×C₄	—	4	2	no	—
276	C₂×C₃×C₄	—	4	2	no	—
277	C₂×C₃×C₄	C₂²⋊Q₈	1	2	yes	—
278	C₂×C₃×C₄	C₂²⋊Q₈	1	2	yes	—
279	C₂×C₃×C₄	#135	1	2	yes	—
280	C₂×C₃×C₄	AGL(1,ℤ/8)	1	2	yes	—
281	C₂×C₃×C₄	#137	1	2	yes	—
282	C₂×C₃×C₄	#137	1	2	yes	—
283	C₂×C₃×C₄	C₂²×Q₈	1	1	yes	characteristic
284	C₂×C₃×C₄	C₂×#41	1	1	yes	characteristic
285	C₂×C₃×C₄	C₂×#41	1	1	yes	characteristic
286	C₂×C₃×C₄	C₂×#41	1	1	yes	characteristic
287	C₂×C₃×C₄	C₂×#41	1	1	yes	characteristic
288	C₂×C₃×C₄	C₂×#41	1	1	yes	characteristic
289	C₃×C₈	—	4	2	no	—
290	C₃×C₈	—	4	2	no	—
291	C₂×Q₈	—	2	1	no	—
292	C₂×Q₈	—	2	1	no	—
293	C₂×Q₈	—	2	1	no	—
294	C₂×Q₈	C₂×C₃×Q₈	1	2	yes	—
295	C₂×Q₈	C₃×#41	1	2	yes	—
296	C₂×Q₈	C₃×#41	1	2	yes	—
297	C₂²×C₄	—	2	1	no	—
298	C₂²×C₄	—	2	1	no	—
299	C₂²×C₄	—	2	1	no	—
300	C₂²×C₄	—	2	1	no	—
301	C₂²×C₄	—	2	2	no	—
302	C₂²×C₄	—	2	2	no	—
303	C₂²×C₄	C₂×C₃×D₄	1	1	yes	characteristic
304	C₂²×C₄	C₂×C₃×D₄	1	1	yes	characteristic
305	C₂²×C₄	C₂×C₃×D₄	1	1	yes	characteristic
306	C₂²×C₄	C₂×C₃×D₄	1	1	yes	characteristic
307	C₂²×C₄	C₂×C₃×D₄	1	1	yes	characteristic
308	C₂²×C₄	C₂×C₃×D₄	1	1	yes	characteristic
309	C₂²×C₄	C₂⁴×C₃	1	1	yes	characteristic
310	C₂×C₈	—	2	2	no	—
311	C₂×C₈	—	2	2	no	—
312	C₂×C₈	—	2	2	no	—
313	C₂×C₈	—	2	2	no	—
314	C₂×C₈	—	2	2	no	—
315	C₂×C₈	—	2	2	no	—
316	C₄⋊C₄	—	2	4	no	—
317	C₄⋊C₄	—	2	4	no	—
318	C₄⋊C₄	—	2	4	no	—
319	C₄⋊C₄	—	2	1	no	—
320	C₄⋊C₄	—	2	1	no	—
321	C₄⋊C₄	—	2	1	no	—
322	C₄⋊C₄	—	2	2	no	—
323	C₄⋊C₄	—	2	2	no	—
324	C₄⋊C₄	—	2	2	no	—
325	C₄⋊C₄	—	2	2	no	—
326	C₄⋊C₄	—	4	2	no	—
327	C₄⋊C₄	—	4	2	no	—
328	C₄⋊C₄	—	4	4	no	—
329	C₄⋊C₄	—	4	2	no	—
330	C₄⋊C₄	—	4	4	no	—
331	C₄⋊C₄	—	4	2	no	—
332	C₄⋊C₄	C₂×C₃×Q₈	1	2	yes	—
333	C₄⋊C₄	C₃×#41	1	2	yes	—
334	C₄⋊C₄	C₃×#41	1	2	yes	—
335	C₄²	—	2	4	no	—
336	C₄²	—	2	4	no	—
337	C₄²	—	2	4	no	—
338	C₄²	—	2	2	no	—
339	C₄²	—	2	2	no	—
340	C₄²	—	2	2	no	—
341	C₄²	—	2	2	no	—
342	C₄²	—	2	1	no	—
343	C₄²	—	2	1	no	—
344	C₄²	—	2	1	no	—
345	C₄²	—	2	1	no	—
346	C₄²	—	4	2	no	—
347	C₄²	—	4	2	no	—
348	C₄²	—	4	2	no	—
349	C₄²	C₂×C₃×Q₈	1	2	yes	—
350	C₄²	C₃×#41	1	2	yes	—
351	C₂²×C₃	C₂×C₂²⋊Q₈	1	1	yes	characteristic
352	C₂²×C₃	#525	1	1	yes	characteristic
353	C₂²×C₃	#525	1	1	yes	characteristic
354	C₂²×C₃	C₂×#135	1	1	yes	characteristic
355	C₂²×C₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
356	C₂²×C₃	C₂×#137	1	1	yes	characteristic
357	C₂²×C₃	C₂×#137	1	1	yes	characteristic
358	C₃×C₄	—	2	2	no	—
359	C₃×C₄	—	2	4	no	—
360	C₃×C₄	—	2	2	no	—
361	C₃×C₄	—	2	2	no	—
362	C₃×C₄	—	4	2	no	—
363	C₃×C₄	—	4	1	no	—
364	C₃×C₄	—	4	2	no	—
365	C₃×C₄	—	4	1	no	—
366	C₃×C₄	—	4	2	no	—
367	C₃×C₄	—	8	2	no	—
368	C₃×C₄	—	8	2	no	—
369	C₃×C₄	#479	1	4	yes	—
370	C₃×C₄	C₂×#125	1	1	yes	characteristic
371	C₃×C₄	#529	1	1	yes	characteristic
372	C₃×C₄	#529	1	1	yes	characteristic
373	C₃×C₄	#533	1	1	yes	characteristic
374	C₂³	C₂²×C₃×D₄	1	1	yes	characteristic
375	Q₈	—	2	2	no	—
376	Q₈	—	2	2	no	—
377	Q₈	—	2	2	no	—
378	Q₈	C₃×#125	1	4	yes	complemented
379	C₂×C₄	—	2	1	no	—
380	C₂×C₄	—	2	1	no	—
381	C₂×C₄	—	2	1	no	—
382	C₂×C₄	—	2	1	no	—
383	C₂×C₄	—	2	2	no	—
384	C₂×C₄	—	2	1	no	—
385	C₂×C₄	—	2	1	no	—
386	C₂×C₄	—	2	2	no	—
387	C₂×C₄	—	2	2	no	—
388	C₂×C₄	—	2	1	no	—
389	C₂×C₄	—	2	1	no	—
390	C₂×C₄	—	2	1	no	—
391	C₂×C₄	—	2	1	no	—
392	C₂×C₄	—	2	2	no	—
393	C₂×C₄	—	2	1	no	—
394	C₂×C₄	—	2	1	no	—
395	C₂×C₄	—	2	2	no	—
396	C₂×C₄	—	2	2	no	—
397	C₂×C₄	—	4	1	no	—
398	C₂×C₄	—	4	1	no	—
399	C₂×C₄	—	4	1	no	—
400	C₂×C₄	—	4	1	no	—
401	C₂×C₄	—	4	1	no	—
402	C₂×C₄	—	4	1	no	—
403	C₂×C₄	—	4	2	no	—
404	C₂×C₄	—	4	2	no	—
405	C₂×C₄	—	4	2	no	—
406	C₂×C₄	—	4	2	no	—
407	C₂×C₄	—	4	2	no	—
408	C₂×C₄	—	4	2	no	—
409	C₂×C₄	C₃×C₂²⋊Q₈	1	2	yes	—
410	C₂×C₄	C₃×C₂²⋊Q₈	1	2	yes	—
411	C₂×C₄	C₃×#135	1	2	yes	—
412	C₂×C₄	C₃×AGL(1,ℤ/8)	1	2	yes	—
413	C₂×C₄	C₃×#137	1	2	yes	—
414	C₂×C₄	C₃×#137	1	2	yes	—
415	C₂×C₄	C₂²×C₃×Q₈	1	1	yes	characteristic
416	C₂×C₄	C₂×C₃×#41	1	1	yes	characteristic
417	C₂×C₄	C₂×C₃×#41	1	1	yes	characteristic
418	C₂×C₄	C₂×C₃×#41	1	1	yes	characteristic
419	C₂×C₄	C₂×C₃×#41	1	1	yes	characteristic
420	C₂×C₄	C₂×C₃×#41	1	1	yes	characteristic
421	C₈	—	4	2	no	—
422	C₈	—	4	2	no	—
423	C₂×C₃	#2851	1	1	yes	characteristic
424	C₂×C₃	C₂×#479	1	1	yes	characteristic
425	C₂×C₃	#3079	1	1	yes	characteristic
426	C₂×C₃	#3106	1	1	yes	characteristic
427	C₂×C₃	#3107	1	1	yes	characteristic
428	C₂×C₃	#3112	1	1	yes	characteristic
429	C₂×C₃	#3113	1	1	yes	characteristic
430	C₂²	C₂×C₃×C₂²⋊Q₈	1	1	yes	characteristic
431	C₂²	C₃×#525	1	1	yes	characteristic
432	C₂²	C₃×#525	1	1	yes	characteristic
433	C₂²	C₂×C₃×#135	1	1	yes	characteristic
434	C₂²	C₂×C₃×AGL(1,ℤ/8)	1	1	yes	characteristic
435	C₂²	C₂×C₃×#137	1	1	yes	characteristic
436	C₂²	C₂×C₃×#137	1	1	yes	characteristic
437	C₄	—	2	2	no	—
438	C₄	—	2	4	no	—
439	C₄	—	2	2	no	—
440	C₄	—	2	2	no	—
441	C₄	—	4	2	no	—
442	C₄	—	4	1	no	—
443	C₄	—	4	2	no	—
444	C₄	—	4	1	no	—
445	C₄	—	4	2	no	—
446	C₄	—	8	2	no	—
447	C₄	—	8	2	no	—
448	C₄	C₃×#479	1	4	yes	—
449	C₄	C₂×C₃×#125	1	1	yes	characteristic
450	C₄	C₃×#529	1	1	yes	characteristic
451	C₄	C₃×#529	1	1	yes	characteristic
452	C₄	C₃×#533	1	1	yes	characteristic
453	C₃	#33073	1	1	yes	characteristic, direct product factor, Sylow
454	C₂	C₃×#2851	1	1	yes	characteristic
455	C₂	C₂×C₃×#479	1	1	yes	characteristic
456	C₂	C₃×#3079	1	1	yes	characteristic
457	C₂	C₃×#3106	1	1	yes	characteristic
458	C₂	C₃×#3107	1	1	yes	characteristic
459	C₂	C₃×#3112	1	1	yes	characteristic
460	C₂	C₃×#3113	1	1	yes	characteristic

	subgroup	G/H
center, socle, prime radical	C₂³×C₃	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₃
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₃ ◁ C₃×C₄³ ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
12. #33073	C₃	direct (N × H)
246. C₃×Q₈	#125	semidirect
378. Q₈	C₃×#125	semidirect
453. C₃	#33073	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₃×#2859	2
C₃×C₄²×Q₈	2
C₃×#1948	2
C₃×#1947	2
C₃×#1920	2
C₃×#1918	2
C₃×#1865	2
C₃×#1863	2
C₃×#1831	2
C₃×#1803	2
#33073	3

Subgroups — C3×#33073 #10651680

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#33073 #10651680